|
|
?????????????????????
?????????????????
???????1???2???2?3?4?5???5???26??
1??
?u???u?u????y?x
du??
2??L?x2?y2?a2????xdy?ydx??
L
?x=3cost?L?3????0?t?2??????????x2+y2?ds=? ?y=3sint.L
4????????dy??fx?y?dx???? ? 2y33
x?y?1
????1)dxdy ?
5??DD
??????????O;????ה???3??
?15??
px0?y0?px0?y0?1?????????????????????fx?y?fx?y?
????? ( )
px0?y0?px0?y0?2???????? ????????????? fx?y?fx?y?
( )
px0?y0?3???????????????fxy(x0,y0)?fyx(x0,y0)?? fx?y?
??? fxy(x0,y0)fyx(0x,0y) ?
L(B,A)( ) ( ) 4?L(A,B)?f(x,y)dx??f(x,y)dx?
5???????????D???????? ?D????( ) fx?y?fx?y?
? 1 ? ? 5 ?
????? ? ???9???45??
1????????????
I??(exsiny?3y)dx?(excosy?3)dy ?
?AO
AO??A(a,0)?O(0,0)???x2?y2?ax???????? ???
???????
???(xV2?y2)dxdydz? ?????z?x2?y2???z?4?????? ? 2 ? ? 5 ?
3??????????
I???dS?
S
??S???x2?y2?z2?R2????z?a(0?a?R)???????z?a??
4??????????
22 I????y(x?z)dydz?xdzdx?(y?xz)dxdy?
S
??S????V??0,b???0,b???0,b??????
? 3 ? ? 5 ?
5??D?(x,y)2?y2?R
????????
?????(???7???14?)
1???????
? 4 ? ? 5 ? ?2?. ????D??????z?e?(x2?y2)???
?(x2?2yz)d?x(2y?2x)z?dy2(?z2?x) ydz
L
???????????????????u(x,y,z)?
2??????????????D???????(?,?)?D, fx?y?
??
????
???????1???2???2?3?4?5???5???26??
1?xyxy??dx?dy? 22222222x?yx?yx?yx?y
2??f(x,Dy)?d?f?(?,?)D S ???SD???D???? 2?2?a?3?54? ? 4??dx?f(x,y)dy?5
?1)? 223X
??????????O;????ה???3???15??
1?? 2???3??4? ? 5?? .
? 5 ? ? 5 ?
?????????12?????
????? ? ? ?
??????1.???????????????????????,????????????????2. ???????????????????????????????????????????
?????????????????????,????????????????????????????????????????.
??? ??????
? ?????
???????????????????u1,u2,?,un??????????????????????????????????????.?
1111?2?3???n?? ??????????1. 2222
??? 1?(?1)?1?(?1)??. ??????
??????? (1?1)?(1?1)?(1?1)?? ?????0?
???? 1?[(?1)?1]?[(?1)?1]??????1.?????????. ?????????????????
??????????.
1?????
??1 ???????un????????????+????????
u1?u2?u3???un?? ?1?
????????????????????un?????1????.
???1??????un???un.
n?1?
2??????
Sn??uk?u1?u2???un??????un??n??????????.
k?1n?1n?
3 ??????
??2??????un???????Sn????S??limSn?S???????
n?1n???
??un?? ??S??????un?????
n?1n?1??
S??un=u1?u2?u3???un??.
n?1?
???????Sn???????????un??.
n?1?
?1 ?????????????
?aqn?1?a?aq?aq2???aqn?1???(a?0)
n?1?
????.
???P2.
?2 ???? 1111??????? 1?22?33?4n(n?1)
????.
???P2.
? ???????
1 ????????
?????un??????????????Sn????????????????
n?1?
??un????Sn????????.???????????an??????????? n?1?
?u
n?1?n?a1?(a2?a1)?(a3?a2)???(an?an?1)??
????????????an????a1?(a2?a1)?(a3?a2)???(an?an?1)??????????????
2 ???????
??1??????Cauchy??? ???1????????????????????
??N????m?N?????????p??? um?1?um?2???um?p??.
?????1???????????????0?0???????N??????? m0(?N),p0??um0?1?um0?2???um0?p0??0.
3?????????
?? ?????? ????1?????
limun?. n??
??????????????????????3.
?3 ??????1?
????.
1?0???? p?m??? n??n??n
1111?????um?1?um?2?um?3???u2m? m?1m?2m?32m
11111??????. ?2m2m2m2m2
1?????0????????N???m?N?p?m?? 2111?????? 23n?????? limun?lim
um0?1?um0?2???um0?p0??0?
???????.
?4 ??????????????? ?
????? um?1?um?2???um?p=111 ????(m?1)2(m?2)2(m?p)21??. n2
?111111???????. m(m?1)(m?1)(m?2)m?p?1)(m?p)mm?pm
1?????0??N?[]???m?N???????p??? ?
1um?1?um?2???um?p???. m
??? ?1??. n2
4 ???????
??2 ????un??vn???????????c,d????(cun?dvn)????
n?1n?1n?1???
? ?(cun?dvn)?c?un?d?vn.
n?1n?1n?1???
???????????????????.
??3 ?????????????????????????.
????????????????????????????.
????un???????S???? un?1?un?2?? ????????
n?1?
???????????Sn??S??????Rn?S?Sn.??????un??n???
n?1?
?.
??4????????????????????????????????. ???????????????????????????????????????.
??(1?1)?(1?1)???(1?1)???0?0???0?????
??? 1?1?1?1??????.
?? P51?2?3?4?5?6?7.
????????? (?????)???? ????
???? ????
?????1.???????????????????2.??????????????????????????????3.????????????????????????????????????
????????????????????????????????????????????????
?????18??
1 ??????
?? ?? ?
1??? ??? ????? ; ?? ( ??? , ? ? ), ? ?
?????? ( ?????????? ). ??????
. 2. ???????? : ????????, ?????????
? . ???????????????? , ???????????????????? .
?1 ??????
????.???????????
?
?, .???? ;
?, ???? ;
?,,
,???? ;
?, , ,???? .
??, ????
0?? ). ????
???, ???
( ?? ?
?2 ????
????.
????????????
?3 ????
????.
??
,
,
=
, .
, .
??, ?????.
?4????
?
????. , . ????.
3. ???????? :
???????{
}, ?? {
}??;
?????{
??,??{
}, ????
, ????, ?
??. =
.}????
?? , ????????????????? .
4.?????????? :
, ??
. ????????? ;
?????, ????
, ??? =
. ??????????.
???? , ??????????? , ??????????? . ????????????? .
?.????????? Cauchy?? ???????{
}???Cauchy?????????? ? ????????Cauchy?? . Th( Cauchy?? )
. ??
?
N,
??????, ????????? ( ?????? ) ?????? , ?????????? . ????? , ??????? . ???
??????
?.
?( ????????? ) ??
.
?5 ??
??
?? .
???????????? . ?
, ??
??
??Cauchy????????? |
???????? ???
|????????? ???
.?6????
( ??
????. .????????????????????? )
?7 ( ??????? ) ??????
?? .
??? ( ?Cauchy????????? )
???
??{
}??. ?????????
. ??
?
.
?? ??????????? ????? ?
??1 ??? Const
????
=
( ????????? )
??
2 ?
?? ?
??, ??
=
?
. ??
: ?
??????????.
?? , ?????????????? ,???? .
( ????????? ) ??3 ???
?8????
??????????? ? ?????????????????? .
2????
?.??????????? :
1. ???? :
2. ???? :
Th 1 ?
??, ?. ???
, ??
. ??
??; ???????????..( ? )
?????????? .
3. ??????????? :
Th 2?
?
?> < ,
< ;?
??????? , ?
??
,
= ?> = ,
.( ?> ??>????? )
?????(??)??-?????-???????????????
?????http://www.850500.com/news/20074.html
?????,??! |
|